NePPO: Near-Potential Policy Optimization for General-Sum Multi-Agent Reinforcement Learning

arXiv:2603.06977 · cs.LG, cs.AI, cs.GT · Submitted 2026-03-07 · Read on arXiv

Listen

Radio episode about this paper

Transcript

Introduction to the show: ident: AI Radio. Generated commentary on the latest Artificial Intelligence papers.

Tom: Today's paper: "NePPO: Near-Potential Policy Optimization for General-Sum Multi-Agent Reinforcement Learning".

Jane: The gist: This paper proposes Near-Potential Policy Optimization (NePPO),

Tom: First, who's behind it and why it matters.

Paper summary: Tom: So we're looking at a paper called "NePPO: Near-Potential Policy Optimization for General-Sum Multi-Agent Reinforcement Learning," and the main idea is trying to train agents in shared environments where everyone has different goals, right?

Jane: That's right. The authors are tackling the problem that training agents in general-sum games gets really unstable, and usually, convergence guarantees only work when things are simple, like a two-player zero-sum game or something fully cooperative

Zhang et al., two thousand twenty-four: or

Zhong et al <ref:2603.06977#pg1>., two thousand twenty-four: <ref:2603.06977#pg1>.

Lu: They propose this new pipeline called Near-Potential Policy Optimization, which tries to compute approximate Nash equilibria in mixed cooperative–competitive environments

Guo et al., 2025a, Maheshwari et al <ref:2603.06977#pg1>., two thousand twenty-four Guo et al <ref:2603.06977#pg1>., two thousand twenty-four 2025b,c: <ref:2603.06977#pg1>.

Meng: So what's the core mechanism here? How does this pipeline actually work to find that equilibrium when you don't have a simple objective function?

Tom: The core idea is to learn a player-independent potential function. They suggest that if you use this potential as the common utility for a cooperative game, its Nash equilibrium will approximate the original game's Nash equilibrium

Guo et al., 2025a, Maheshwari et al <ref:2603.06977#pg1>., two thousand twenty-four: <ref:2603.06977#pg1>.

Jane: That sounds complicated because it involves learning something independent of any single player’s specific strategy. They introduce what they call Markov Near-Potential Functions or MNPFs, which are functions that approximate the change in each agent’s value when one agent makes a unilateral deviation

Guo et al., 2025a, Maheshwari et al <ref:2603.06977#pg1>., two thousand twenty-four: <ref:2603.06977#pg1>.

Lu: The key property of this framework is that if you maximize this potential function, you get an approximate Nash equilibrium of the original game

Guo et al., 2025b: <ref:2603.06977#pg1>.

Tom: But they realize optimizing over agents directly is infinite-dimensional and non-smooth. So they have to restrict the candidate potential function to a parameterized family, w, with a parameter vector w in R p

Guo et al., 2025b: <ref:2603.06977#pg1>.

Meng: How do you handle that infinite maximization problem when you're trying to learn it through reinforcement learning? Is there a simple way to make it tractable?

Tom: They address the non-smoothness by replacing the maximization over agents with a smooth approximation, beta, which they define as one/beta sum i=N e beta F i

Guo et al., 2025b: <ref:2603.06977#pg1>.

Paper summary: Jane: That's using the log-sum-exp trick to smooth out the maximization, which is a standard technique in these kinds of problems. And then they frame it as minimizing this smoothed objective, w F(w), which they solve using Algorithm one

Guo et al., 2025b: <ref:2603.06977#pg1>.

Lu: Algorithm one has three parts: a gradient-descent module, estimating that smooth function beta(w), and the iterative process itself

Guo et al., 2025b: <ref:2603.06977#pg1>. The gradient estimation part uses a two-point estimator to avoid that tough bilevel optimization structure where one function depends on another strategy pi*, and another one depends on a different strategy pi* J i

Guo et al., 2025b: <ref:2603.06977#pg1>.

Meng: That sounds like a lot of computation. What does that mean for deployment? How much do we have to compute just to get an update?

Tom: Well, the gradient estimation part is where they circumvent that dependency on the strategies, which is crucial because F i depends on pi*, and pi* J i

Guo et al., 2025b: <ref:2603.06977#pg1>. Module M1 then uses standard gradient descent to solve the objective, while Module M2 requires computing approximate Nash equilibria of cooperative games using CoopGameSolver and best responses using RLSolver

Guo et al., 2025b: <ref:2603.06977#pg1>.

Jane: So, to summarize, they are learning a potential function w that minimizes the smoothed objective function beta(w), and this optimization is done iteratively using gradient descent guided by solvers for cooperative games

Guo et al., 2025b: <ref:2603.06977#pg1>.

Lu: They show that if the maximum value of F i is less than some value alpha, then the resulting policy pi* is an alpha-Nash equilibrium

Guo et al., 2025b: <ref:2603.06977#pg1>. And they prove that a game structure G about sharing the same structure as the original game G, and all players in G about use an MNPF of G, with approximation parameter alpha, means the policy pi about is an alpha-approximate Nash equilibrium of the original game

Guo et al., 2025b: <ref:2603.06977#pg1>.

Tom: That's a solid theoretical link there. It suggests that minimizing that maximum value across players is enough to get you close to a Nash equilibrium

Guo et al., 2025b: <ref:2603.06977#pg1>. The structural property they find in Proposition three point two is interesting because it says if a game G is already a Markov potential game with potential function, then F i is zero for all agents i

Guo et al., 2025b: <ref:2603.06977#pg1>.

Paper summary: Jane: That's an important structural finding. It means that even if the game isn't a standard potential game, there are still games where those values are zero for every agent, which opens up new possibilities

Guo et al., 2025b: <ref:2603.06977#pg1>. This is what makes the framework more versatile than just relying on standard potential games.

Lu: The experimental evaluation shows they tested this on two types of problems: a class of two-player, two-action matrix games and a generalsum partially observable dynamic game based on the Simple World Comm benchmark

Guo et al., 2025c: <ref:2603.06977#pg1>.

Meng: I'm curious about the practical side. How did it do when compared to the established methods like IPPO and MAPPO? Did it just match them, or was there a real improvement in performance?

Tom: They compared it on matrix games and found that NePPO consistently achieved the lowest regret across all values of alpha, and in several cases, it actually recovered exact Nash equilibria

Guo et al., 2025c: <ref:2603.06977#pg1>.

Jane: And even on that partially observable dynamic game, where the environment is more complex, NePPO significantly outperformed all baselines by minimizing Nash regret

Guo et al., 2025c: <ref:2603.06977#pg1>. It seems to explicitly target regret minimization by aligning local unilateral deviations through that learned potential function

Guo et al., 2025c: <ref:2603.06977#pg1>.

Lu: The conclusion they draw is that this new MARL algorithm, NePPO, successfully approximates Nash equilibria in general-sum games by learning a shared potential function that captures changes in players’ utilities under unilateral best-response deviations

Guo et al., 2025b: <ref:2603.06977#pg1>.

Tom: It works across a range of settings, even in zerosum games where no global potential function exists

Guo et al., 2025c: <ref:2603.06977#pg1>. That's a big deal for general-sum problems.

Jane: Yes, and they show it recovers the right Nash equilibrium in complex environments where other methods fail

Guo et al., 2025c: <ref:2603.06977#pg1>. But the authors also mention that future work includes establishing convergence guarantees for Algorithm one's training dynamics

Guo et al., 2025b: , developing first-order gradient estimators to improve sample efficiency, and designing principled parameterizations of the potential function to serve as a design handle for equilibrium selection

Guo et al <ref:2603.06977#pg1>., 2025b: <ref:2603.06977#pg1>.

Lu: That last point about parameterizing is where I think the real power lies. It turns learning into a more structured design problem for selecting which equilibrium you want to approximate

Guo et al., 2025b: <ref:2603.06977#pg1>.

Paper summary: Meng: From my side, what I'm thinking is that if we deploy this on a large-scale system, how much overhead does it introduce compared to just running one of the existing baselines? Is it too much complexity for production?

Tom: The paper focuses more on the performance gain in terms of regret minimization across different game structures than on deployment cost. But they are showing that it’s a way to balance those competitive and cooperative objectives

Guo et al., 2025c: <ref:2603.06977#pg1>.

Jane: So, while the theory suggests this is a robust way to handle heterogeneous preferences, the immediate next step for researchers is figuring out how to make the training process more sample-efficient and how to choose the right potential function parameters

Guo et al., 2025b: <ref:2603.06977#pg1>.

Lu: It seems like they've found a way to use a structure—the potential function—to guide learning toward an equilibrium, even when there's no simple utility function guiding everyone simultaneously.

Meng: It definitely suggests that for complex environments where we can't define a perfect global objective, this kind of structural approach might be more reliable than just tuning hyperparameters on existing algorithms

Guo et al., 2025c: <ref:2603.06977#pg1>.

Tom: Yeah, it’s about learning the structure of equilibrium itself rather than just chasing a single point in the training loss landscape

Guo et al., 2025c: <ref:2603.06977#pg1>.

Jane: So to wrap up on "NePPO: Near-Potential Policy Optimization for General-Sum Multi-Agent Reinforcement Learning," it gives us a new pipeline to find approximate Nash equilibria by learning a player-independent potential function, and the results show it performs better than IPPO and MAPPO in both matrix games and complex dynamic games

Guo et al., 2025c: <ref:2603.06977#pg1>.

Lu: It’s a step toward handling the messy reality of real-world autonomous systems where agents aren't always perfectly cooperative

Guo et al., 2025b: <ref:2603.06977#pg1>.

Meng: The main limitation they flag is that they are still developing convergence guarantees for Algorithm one so we can't deploy it yet without more stability proofs

Guo et al., 2025b: <ref:2603.06977#pg1>.

Tom: So the idea is promising, but the next phase is proving that the whole training process actually stabilizes at scale

Guo et al., 2025c: <ref:2603.06977#pg1>.

Jane: That’s right. It’s a solid paper for anyone trying to build learning systems for agents with conflicting goals

Guo et al., 2025b: <ref:2603.06977#pg1>.

Conclusion: Tom: So we're wrapping up on NePPO, which stands for Near-Potential Policy Optimization for General-Sum Multi-Agent Reinforcement Learning

Guo et al., 2025b: <ref:2603.06977#pg1>.

Jane: Basically, the paper proposes a new way to train agents in games where everyone has different goals by learning one shared potential function.

Tom: Right, it's about finding an approximate Nash equilibrium in these messy cooperative and competitive situations. The authors are trying to solve the problem of what system-level objective even matters when agents disagree on what they want.

Jane: They tackle that by learning a player-independent function, which they call Markov Near-Potential Functions, or MNPFs. It’s like finding a common metric that describes how much each agent’s outcome changes when another agent makes a move.

Lu: The core idea is that if you use this potential as the common utility for one type of game, its equilibrium will get close to the original game's Nash equilibrium

Guo et al., 2025b: <ref:2603.06977#pg1>.

Meng: So, what does this actually mean for deployment? Because we usually need a clean objective function to train a model.

Tom: It means they’ve found a way around that by using this potential function to guide the learning process, even when you don't have a single perfect global utility.

Jane: And they do it by replacing the hard maximization over all agents with a smoother approximation, which helps the learning algorithm run without getting stuck

Guo et al., 2025b: <ref:2603.06977#pg1>.

Lu: They show mathematically that if the maximum value of these functions is below some threshold alpha, then the resulting policy is an approximate Nash equilibrium

Guo et al., 2025b: <ref:2603.06977#pg1>.

Meng: That sounds like it could be useful for complex systems where we can't even define a single objective. But what about running this on a real-world setup?

Tom: The experiments show that NePPO beats popular methods like IPPO and MAPPO in both matrix games and these more complicated dynamic games

Guo et al., 2025c: <ref:2603.06977#pg1>.

Jane: It really shows how targeting regret minimization through this potential function helps the AI balance those conflicting competitive and cooperative goals.

Lu: And they found a structural property where if a game already has a certain structure, the values for these functions become zero, which is an interesting mathematical finding

Guo et al., 2025b: <ref:2603.06977#pg1>.

Tom: So, NePPO gives us a pipeline to approximate Nash equilibria in general-sum games using this potential function approach.

Jane: It's a step toward handling those tricky real-world scenarios where agents are not always cooperating perfectly. But the next big thing for this work is figuring out how to make the training dynamics stable and efficient enough for actual production use

Guo et al., 2025b: <ref:2603.06977#pg1>.

Addison Kalanther, Sanika Bharvirkar, Shankar Sastry, Chinmay Maheshwari

Electrical Engineering and Computer Sciences, UC Berkeley · Electrical and Computer Engineering, Data Science & Artificial Intelligence Institute, Johns Hopkins University

cs.LG, cs.AI, cs.GT

Submitted: 2026-03-07

Updated: 2026-10-13

Comments: Accepted to the IEEE Conference on Decision and Control (CDC) 2026

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 81/100

The gist: The gist: This paper proposes Near-Potential Policy Optimization (NePPO), a novel Multi-Agent Reinforcement Learning (MARL) pipeline that learns a player-independent potential function to compute

Key concepts

Near-Potential Policy Optimization (NePPO)
A novel MARL pipeline that learns a shared, player-independent potential function. This function helps approximate Nash equilibria in mixed cooperative and competitive environments by capturing how individual utilities react to unilateral deviations, guiding the learning process toward a stable equilibrium.
Markov Near-Potential Functions (MNPFs)
These are player-independent functions used to approximate the change in an agent's value when they deviate from their current strategy. The framework relies on finding an MNPF that relates to the potential function, which is key for identifying approximate Nash equilibria in general-sum games.
Potential Function ($\Phi$)
A player-independent function learned by the algorithm. The core idea is that a maximizer of this potential function corresponds to an approximate Nash equilibrium of the original game. Learning this function allows the system to balance conflicting agent preferences by focusing on a shared, underlying structure.
Zeroth-Order Gradient Descent
A specific optimization technique used in NePPO to minimize the objective function involving the potential function. This method is employed because directly calculating gradients through the complex bilevel optimization structure is difficult; instead, it uses estimators that approximate these gradients to iteratively improve the policy.

Terminology

Summary

The gist: This paper proposes Near-Potential Policy Optimization (NePPO), a novel Multi-Agent Reinforcement Learning (MARL) pipeline that learns a player-independent potential function to compute approximate Nash equilibria in general-sum games with heterogeneous preferences.

Introduction and Problem Statement

Multi-agent reinforcement learning (MARL) is increasingly used to design learning-enabled agents that interact in shared environments, but training MARL algorithms in generalsum games remains challenging because learning dynamics can become unstable, and convergence guarantees typically hold only in restricted settings such as two-player zero-sum or fully cooperative games<ref:2603.06977#pg2>. Moreover, when agents have heterogeneous and potentially conflicting preferences, it is unclear what system-level objective should guide learning<ref:2603.06977#pg2>. The paper addresses this challenge through the framework of Markov Near-Potential Functions (MNPFs), where an MNPF is a player-independent function that approximates the change in each agent’s value induced by unilateral deviations<ref:2603.06977#pg3>. A key property of this framework is that a maximizer of the potential function corresponds to an approximate Nash equilibrium of the original game<ref:2603.06977#pg4>.

Near-Potential Policy Optimization Algorithm

The core idea involves learning a potential function and using it to compute approximate Nash equilibria<ref:2603.06977#pg5>. The proposed MARL pipeline aims to solve the optimization problem min Φ:Π→R F(Φ) = max i∈N Fi(Φ), which is infinite-dimensional and nonsmooth<ref:2603.06977#pg6>. To make this tractable, the candidate potential function is restricted to a parameterized family Φw: Π → R, where w ∈ W ⊂ R p is a parameter vector<ref:2603.06977#pg6>. The non-smoothness introduced by the maximization over agents is addressed by replacing maxi∈N Fi(Φ) with the smooth approximation F˜β(Φ):= 1/β log X i∈N exp(βFi(Φ))!, where ties are broken arbitrarily<ref:2603.06977#pg6>. The final optimization problem solved is min w∈W F˜β(Φw), which is tackled using Algorithm 1<ref:2603.06977#pg6>.

Algorithm 1 consists of three main modules: (M1) Gradient-descent module, (M2) Estimating F˜β(Φw), and the iterative process itself<ref:2603.06977#pg6>. The gradient estimation employs a two-point estimator to circumvent the bilevel optimization structure arising from Fi(Φ) depending on π∗,Φ and π∗,Ji<ref:2603.06977#pg6>. Module (M1) uses gradient descent to solve the objective, while Module (M2) requires computing approximate Nash equilibria of cooperative games using CoopGameSolver and best responses using RLSolver<ref:2603.06977#pg6>.

Theoretical Guarantees and Key Results

Theorem 3.1 states that if maxi Fi(Φ) ≤ α, then π∗,Φ is an α-Nash equilibrium<ref:2603.06977#pg6>. This ensures that minimizing the maximum value of Fi across players is enough to approximate a Nash equilibrium<ref:2603.06977#pg6>. Proposition 2.3 shows that if a game G˜ shares the same structure as G, and all players in G˜ share the same utility function equal to an MNPF Φ of G with approximation parameter α, then π˜ will be an α-approximate Nash equilibrium of the original game G<ref:2603.06977#pg5>.

A structural property is highlighted in Proposition 3.2, which establishes that if a game G is a Markov potential game with potential function Φ, then Fi(Φ) = 0 for all i ∈ N<ref:2603.06977#pg6>. Furthermore, the paper demonstrates that there exist games that are not potential games but satisfy Fi(Φ) = 0 for every i ∈ N<ref:2603.06977#pg6>.

Experimental Evaluation

The algorithm is evaluated on two classes of problems: a class of two-player, two-action matrix games and a generalsum partially observable dynamic game based on the Simple World Comm benchmark<ref:2603.06977#pg9>. In the toy example, Algorithm 1 successfully recovers the Nash equilibrium where MAPPO converges to an incorrect strategy<ref:2603.06977#pg9>.

When compared against popular baselines like IPPO and MAPPO on the matrix games, NePPO consistently achieves the lowest regret across all values of α, and in several cases recovers exact Nash equilibria<ref:2603.06977#pg10>. In the partially observable dynamic game, NePPO significantly outperforms all baselines by minimizing Nash regret<ref:2603.06977#pg9>. The results show that NePPO explicitly targets regret minimization by aligning local unilateral deviations through the learned potential function, enabling it to balance competitive and cooperative objectives<ref:2603.06977#pg9>.

Conclusions

In this paper, a new MARL algorithm for approximating Nash equilibria in generalsum games is proposed by learning a shared potential function that captures changes in players’ utilities under unilateral best-response deviations<ref:2603.06977#pg6>. This approach achieves low-regret approximate Nash equilibria across a range of settings, including zerosum games where no global potential function exists<ref:2603.06977#pg9>. Future work includes establishing convergence guarantees for the training dynamics of Algorithm 1, developing first-order gradient estimators to improve sample efficiency, and designing principled parameterizations of the potential function Φ to serve as a design handle for equilibrium selection<ref:2603.06977#pg6>. The paper concludes by showing that NePPO successfully recovers the right Nash equilibrium in complex environments where other methods fail<ref:2603.06977#pg9>.

Improvements for AI systems

  1. A new MARL pipeline called Near-Potential Policy Optimization (NePPO) can be used to compute approximate Nash equilibria in mixed cooperative–competitive environments by learning a player-independent potential function such that the Nash equilibrium of a cooperative game with this potential as the common utility approximates a Nash equilibrium of the original game.

  2. The NePPO approach allows for the tunable design handle provided by parameterizing the potential function, allowing researchers to encode system-level objectives directly through the representation of Φ without modifying individual agents’ reward functions.

  3. The system can solve complex general-sum games by minimizing a novel objective, which is defined such that if, for some Φ, this discrepancy is bounded by α ≥ 0, for every player, then π∗,Φ constitutes an α-approximate Nash equilibrium of the original game (Theorem 3.1).

  4. The algorithm can be implemented modularly using HAPPO [Zhong et al., 2024] for solving the cooperative MARL problem and PPO [Schulman et al., 2017] for computing approximate best responses, enabling a unified training pipeline.

  5. In partially observable dynamic games (POMGs), NePPO can be applied by parameterizing the potential function as an infinite-horizon discounted sum of a learned stage reward ϕw, allowing it to balance competitive and cooperative objectives in scenarios like the Simple World Comm benchmark.

Sources

Related papers